Certain stationary exercise machines with reciprocating leg and/or arm portions have been developed. Such stationary exercise machines include stair climbers and elliptical trainers, each of which typically offers a different type of workout. For example, a stair climber may provide a lower frequency vertical climbing simulation while an elliptical trainer may provide a higher frequency horizontal running simulation. Additionally, these machines may include handles that provide support for the user's arms during exercise. However, the connections between the handles and leg portions of traditional stationary exercise machines may not enable sufficient exercise of the user's upper body. Also, existing stationary exercise machines typically have minimal adjustability mainly limited to adjusting the amount of resistance applied to the reciprocating leg portions. It may therefore be desirable to provide an improved stationary exercise machine which addresses one or more of the problems in the field and which generally improves the user experience.